from my understanding, 4' and under doesnt require a centre brace. the tank isnt long enough to "dip" in the middle. providing you have you stand and floor in which it sits, level. i used 0.5" plywood for the top and bottom too so i personally think thats fine. i would however use 0.75" plywood for the wrap. the wrap will add stability to your stand
going what the "the king of diy" on youtube "a 2x4 will hold around 800lbs of weight" so technically your stand will support the weight without any problems.
you can also add some foam padding or use styrofoam under your tank to adjust any slight imperfections on level, marine depot sells the "proper" aquarium foams, but its your call.
honestly, your stand looks pretty hardcore. if you're worried but dont want to the centre leg then you can add two legs closer to the inside. on a 4' tank id say 20" on each side. gives you a 28" opening in the middle. not the biggest, but should be enough. this will shorten your length of the tank that could dip. if you can sleep tonight without worrying about it, then i would leave it lol
good luck